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Submission #947708

# Submission time Handle Problem Language Result Execution time Memory
947708 2024-03-16T22:35:57 Z chroot_ Skyscraper (JOI16_skyscraper) C++14
100 / 100
 475 ms 192088 KB 
#include <bits/stdc++.h>
using namespace std;

using LL = long long;
using PII = pair<int, int>;

const int N = 105, V = 3005;
const int M = 1e9 + 7;

LL dp[N][N][V][2][2], a[N];

int main() {
    ios::sync_with_stdio(0);
    cin.tie(0);

    int n, L;
    cin >> n >> L;

    for(int i = 1; i <= n; i++) cin >> a[i];
    sort(a + 1, a + 1 + n), a[n + 1] = 2004;
    int d = a[2] - a[1];

    dp[1][1][0][0][0] = 1, dp[1][1][d][1][0] = 1;
    dp[1][1][d][0][1] = 1, dp[1][1][d * 2][1][1] = 1;

    for(int i = 1; i <= n; i++) {
        for(int j = 1; j <= i; j++) {
            for(int sum = 0; sum <= L; sum++) {
                for(int l = 0; l <= 1; l++) {
                    for(int r = 0; r <= 1; r++) {

                        // place a new component in the middle
                        int new_sum = sum + (j * 2 + l + r) * (a[i + 2] - a[i + 1]);
                        dp[i + 1][j + 1][new_sum][l][r] += dp[i][j][sum][l][r] * (j - 1) % M;
                        dp[i + 1][j + 1][new_sum][l][r] %= M;

                        //place a new component in the left , don't block it
                        if(l > 0){
                            new_sum = sum + (j * 2 + l + r) * (a[i + 2] - a[i + 1]);
                            dp[i + 1][j + 1][new_sum][l][r] += dp[i][j][sum][l][r];
                            dp[i + 1][j + 1][new_sum][l][r] %= M;
                        }

                        //place a new component in the left and block it
                        if(l > 0){
                            new_sum = sum + (j * 2 + r) * (a[i + 2] - a[i + 1]);
                            dp[i + 1][j + 1][new_sum][0][r] += dp[i][j][sum][l][r];
                            dp[i + 1][j + 1][new_sum][0][r] %= M;
                        }

                        //place a new component in the right, don't block it
                        if(r > 0){
                            new_sum = sum + (j * 2 + l + r) * (a[i + 2] - a[i + 1]);
                            dp[i + 1][j + 1][new_sum][l][r] += dp[i][j][sum][l][r];
                            dp[i + 1][j + 1][new_sum][l][r] %= M;
                        }

                        //place a new component in the right and block it
                        if(r > 0){
                            new_sum = sum + (j * 2 + l) * (a[i + 2] - a[i + 1]);
                            dp[i + 1][j + 1][new_sum][l][0] += dp[i][j][sum][l][r];
                            dp[i + 1][j + 1][new_sum][l][0] %= M;
                        }

                        //add to existing component but not at the end of permutation
                        new_sum = sum + ((j - 1) * 2  + l + r) * (a[i + 2] - a[i + 1]);
                        dp[i + 1][j][new_sum][l][r] += dp[i][j][sum][l][r] * (j - 1 ) * 2 % M;
                        dp[i + 1][j][new_sum][l][r] %= M;

                        //adding to left of the leftmost component but do not block it
                        if(l > 0){
                            new_sum = sum + ((j - 1) * 2  + l + r) * (a[i + 2] - a[i + 1]);
                            dp[i + 1][j][new_sum][l][r] += dp[i][j][sum][l][r];
                            dp[i + 1][j][new_sum][l][r] %= M;
                        }

                        //adding to left of the leftmost component and block it
                        if(l > 0){
                            new_sum = sum + ((j - 1) * 2  + l + r - 1) * (a[i + 2] - a[i + 1]);
                            dp[i + 1][j][new_sum][0][r] += dp[i][j][sum][l][r];
                            dp[i + 1][j][new_sum][0][r] %= M;
                        }

                        //adding to right of the rightmost component but do not block it
                        if(r > 0){
                            new_sum = sum + ((j - 1) * 2  + l + r) * (a[i + 2] - a[i + 1]);
                            dp[i + 1][j][new_sum][l][r] += dp[i][j][sum][l][r];
                            dp[i + 1][j][new_sum][l][r] %= M;
                        }

                        //adding to right of the rightmost component and block it
                        if(r > 0){
                            new_sum = sum + ((j - 1) * 2  + l + r - 1) * (a[i + 2] - a[i + 1]);
                            dp[i + 1][j][new_sum][l][0] += dp[i][j][sum][l][r];
                            dp[i + 1][j][new_sum][l][0] %= M;
                        }

                        //merging two components
                        if(j > 1 ) {
                            new_sum = sum + ((j - 2 ) * 2 + l + r) * (a[i + 2] - a[i + 1]);
                            dp[i + 1][j - 1][new_sum][l][r] += dp[i][j][sum][l][r] * (j - 1)%M;
                            dp[i + 1][j - 1][new_sum][l][r] %= M;
                        }

                    }
                }
            }
        }
    }

    LL ans = 0;
    for(int sum = 0; sum <= L; sum++) ans = (ans + dp[n][1][sum][0][0]) % M;
    cout << ans; 
}

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2396 KB Output is correct
2 Correct 1 ms 2396 KB Output is correct
3 Correct 1 ms 2396 KB Output is correct
4 Correct 1 ms 2652 KB Output is correct
5 Correct 4 ms 4952 KB Output is correct
6 Correct 4 ms 4700 KB Output is correct
7 Correct 1 ms 2908 KB Output is correct
8 Correct 1 ms 2908 KB Output is correct
9 Correct 4 ms 4700 KB Output is correct
10 Correct 1 ms 2908 KB Output is correct

Subtask #2
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 3164 KB Output is correct
2 Correct 2 ms 3676 KB Output is correct
3 Correct 1 ms 3160 KB Output is correct
4 Correct 3 ms 3676 KB Output is correct
5 Correct 3 ms 3676 KB Output is correct
6 Correct 2 ms 3420 KB Output is correct
7 Correct 1 ms 3164 KB Output is correct
8 Correct 1 ms 3164 KB Output is correct
9 Correct 2 ms 3420 KB Output is correct
10 Correct 2 ms 3420 KB Output is correct

Subtask #3
80.0 / 80.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2396 KB Output is correct
2 Correct 1 ms 2396 KB Output is correct
3 Correct 1 ms 2396 KB Output is correct
4 Correct 1 ms 2652 KB Output is correct
5 Correct 4 ms 4952 KB Output is correct
6 Correct 4 ms 4700 KB Output is correct
7 Correct 1 ms 2908 KB Output is correct
8 Correct 1 ms 2908 KB Output is correct
9 Correct 4 ms 4700 KB Output is correct
10 Correct 1 ms 2908 KB Output is correct
11 Correct 1 ms 3164 KB Output is correct
12 Correct 2 ms 3676 KB Output is correct
13 Correct 1 ms 3160 KB Output is correct
14 Correct 3 ms 3676 KB Output is correct
15 Correct 3 ms 3676 KB Output is correct
16 Correct 2 ms 3420 KB Output is correct
17 Correct 1 ms 3164 KB Output is correct
18 Correct 1 ms 3164 KB Output is correct
19 Correct 2 ms 3420 KB Output is correct
20 Correct 2 ms 3420 KB Output is correct
21 Correct 6 ms 7768 KB Output is correct
22 Correct 240 ms 100948 KB Output is correct
23 Correct 470 ms 189268 KB Output is correct
24 Correct 362 ms 149764 KB Output is correct
25 Correct 465 ms 191316 KB Output is correct
26 Correct 400 ms 167216 KB Output is correct
27 Correct 125 ms 66132 KB Output is correct
28 Correct 149 ms 75228 KB Output is correct
29 Correct 280 ms 120756 KB Output is correct
30 Correct 475 ms 192088 KB Output is correct